Understanding Function Intervals and Relative Extrema

This video tutorial explains how to determine the intervals where a function is increasing or decreasing and how to identify relative extrema by analyzing the graph of the function without using calculus techniques. It includes examples using a graphing calculator to analyze quadratic and cubic functions, demonstrating how to find relative minima and maxima and determine the intervals of increase and decrease.

What is the main focus of the lesson in the video?

• Using calculus to find function intervals

• Determining intervals where a function is increasing or decreasing and identifying relative extrema

• Graphing linear functions

• Solving quadratic equations

When is a function considered to be increasing on an open interval?

• When for any x1 and x2 in the interval, if x2 is greater than x1, then f(x2) is less than f(x1)

• When for any x1 and x2 in the interval, if x2 is greater than x1, then f(x2) is equal to f(x1)

• When for any x1 and x2 in the interval, if x2 is greater than x1, then f(x2) is greater than f(x1)

• When for any x1 and x2 in the interval, if x2 is less than x1, then f(x2) is greater than f(x1)

What happens to the graph of a function when it is decreasing on an open interval?

• The graph oscillates

• The graph remains constant

• The graph moves downward from left to right

• The graph moves upward from left to right

Where do relative extrema occur?

• Where a function has a horizontal tangent

• Where a function changes from increasing to decreasing or from decreasing to increasing

• Where a function is constant

• Where a function has a vertical tangent

What is the relative minimum point found in the quadratic function example?

• (0, -5)

• (1, 5)

• (2, -5)

• (1, -5)

On which interval is the quadratic function decreasing?

• From 2 to positive infinity

• From 1 to positive infinity

• From 1 to 2

• From negative infinity to 1

What type of function is used in the second example?

• Exponential function

• Linear function

• Cubic function

• Quadratic function

What is the relative maximum point found in the cubic function example?

• (1, 2)

• (2, 1)

• (1, -2)

• (2, -1)

On which interval is the cubic function increasing?

• From negative infinity to 2

• From negative infinity to 1 and from 2 to positive infinity

• From 2 to positive infinity

• From 1 to 2

What is the relative minimum point found in the cubic function example?

• (1, 2)

• (2, 1)

• (1, -2)

• (2, -1)